Abstract
Dynamic programming is used to develop and apply an energy optimal control algorithm for urban transportation systems, in which most vehicles reach the next station on time and where departure times vary soon after disoatching. The optimization problem is formulated with control and states constraints, then its solution is developed using dynamic programming procedures. Applying this technique of energy optimal control to the metro network in Hamburg (West Germany) the transport authority would save energy of some 8 x 106kWh per year. With the aid of the control algorithm developed here, it is for the first time easily possible to run urban transit systems safely and automatically on a strict time-table and thereby minimizing energy consumption.
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